Direct and Inverse Inequalities for Jackson Polynomials of 2n- Periodic Bounded Measurable Functions in Locally Clobal Norms

Convergence properties of Jackson polynomials have been considered by Zugmund [1,ch.X] in (1959) and J.Szbados [2], (p=oo) while in (1983) V.A.Popov and J.Szabados [3] (1leq p leq o) have proved a direct inequality for Jackson polynomials in Lp-sp ace of 2n- periodic bounded Riemann integrable functions (f in R) in terms of some modulus of continuity . In 1991 S.K.Jassim proved direct and inverse inequality for Jackson polynomials in locally global norms (Lvarphi,) of 2pi-periodic bounded measurable functions (f in Loo) in terms of suitable Peetre K-functional [4]. Now the aim of our paper is to proved direct and inverse inequalities for Jackson polynomials of (f Lin) in (Lvarphi,p) in terms of the average modulus of continuity .